models/research/neural_gpu/neural_gpu.py

# Copyright 2015 Google Inc. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ==============================================================================
"""The Neural GPU Model."""

import time

import numpy as np
from six.moves import xrange
import tensorflow as tf

from tensorflow.python.framework import function
import data_utils as data

do_jit = False  # Gives more speed but experimental for now.
jit_scope = tf.contrib.compiler.jit.experimental_jit_scope


def conv_linear(args, kw, kh, nin, nout, rate, do_bias, bias_start, prefix):
  """Convolutional linear map."""
  if not isinstance(args, (list, tuple)):
    args = [args]
  with tf.variable_scope(prefix):
    with tf.device("/cpu:0"):
      k = tf.get_variable("CvK", [kw, kh, nin, nout])
    if len(args) == 1:
      arg = args[0]
    else:
      arg = tf.concat(axis=3, values=args)
    res = tf.nn.convolution(arg, k, dilation_rate=(rate, 1), padding="SAME")
    if not do_bias: return res
    with tf.device("/cpu:0"):
      bias_term = tf.get_variable(
          "CvB", [nout], initializer=tf.constant_initializer(bias_start))
    bias_term = tf.reshape(bias_term, [1, 1, 1, nout])
    return res + bias_term


def sigmoid_cutoff(x, cutoff):
  """Sigmoid with cutoff, e.g., 1.2sigmoid(x) - 0.1."""
  y = tf.sigmoid(x)
  if cutoff < 1.01: return y
  d = (cutoff - 1.0) / 2.0
  return tf.minimum(1.0, tf.maximum(0.0, cutoff * y - d), name="cutoff_min")


@function.Defun(tf.float32, noinline=True)
def sigmoid_cutoff_12(x):
  """Sigmoid with cutoff 1.2, specialized for speed and memory use."""
  y = tf.sigmoid(x)
  return tf.minimum(1.0, tf.maximum(0.0, 1.2 * y - 0.1), name="cutoff_min_12")


@function.Defun(tf.float32, noinline=True)
def sigmoid_hard(x):
  """Hard sigmoid."""
  return tf.minimum(1.0, tf.maximum(0.0, 0.25 * x + 0.5))


def place_at14(decided, selected, it):
  """Place selected at it-th coordinate of decided, dim=1 of 4."""
  slice1 = decided[:, :it, :, :]
  slice2 = decided[:, it + 1:, :, :]
  return tf.concat(axis=1, values=[slice1, selected, slice2])


def place_at13(decided, selected, it):
  """Place selected at it-th coordinate of decided, dim=1 of 3."""
  slice1 = decided[:, :it, :]
  slice2 = decided[:, it + 1:, :]
  return tf.concat(axis=1, values=[slice1, selected, slice2])


def tanh_cutoff(x, cutoff):
  """Tanh with cutoff, e.g., 1.1tanh(x) cut to [-1. 1]."""
  y = tf.tanh(x)
  if cutoff < 1.01: return y
  d = (cutoff - 1.0) / 2.0
  return tf.minimum(1.0, tf.maximum(-1.0, (1.0 + d) * y))


@function.Defun(tf.float32, noinline=True)
def tanh_hard(x):
  """Hard tanh."""
  return tf.minimum(1.0, tf.maximum(0.0, x))


def layer_norm(x, nmaps, prefix, epsilon=1e-5):
  """Layer normalize the 4D tensor x, averaging over the last dimension."""
  with tf.variable_scope(prefix):
    scale = tf.get_variable("layer_norm_scale", [nmaps],
                            initializer=tf.ones_initializer())
    bias = tf.get_variable("layer_norm_bias", [nmaps],
                           initializer=tf.zeros_initializer())
    mean, variance = tf.nn.moments(x, [3], keep_dims=True)
    norm_x = (x - mean) / tf.sqrt(variance + epsilon)
    return norm_x * scale + bias


def conv_gru(inpts, mem, kw, kh, nmaps, rate, cutoff, prefix, do_layer_norm,
             args_len=None):
  """Convolutional GRU."""
  def conv_lin(args, suffix, bias_start):
    total_args_len = args_len or len(args) * nmaps
    res = conv_linear(args, kw, kh, total_args_len, nmaps, rate, True,
                      bias_start, prefix + "/" + suffix)
    if do_layer_norm:
      return layer_norm(res, nmaps, prefix + "/" + suffix)
    else:
      return res
  if cutoff == 1.2:
    reset = sigmoid_cutoff_12(conv_lin(inpts + [mem], "r", 1.0))
    gate = sigmoid_cutoff_12(conv_lin(inpts + [mem], "g", 1.0))
  elif cutoff > 10:
    reset = sigmoid_hard(conv_lin(inpts + [mem], "r", 1.0))
    gate = sigmoid_hard(conv_lin(inpts + [mem], "g", 1.0))
  else:
    reset = sigmoid_cutoff(conv_lin(inpts + [mem], "r", 1.0), cutoff)
    gate = sigmoid_cutoff(conv_lin(inpts + [mem], "g", 1.0), cutoff)
  if cutoff > 10:
    candidate = tanh_hard(conv_lin(inpts + [reset * mem], "c", 0.0))
  else:
    # candidate = tanh_cutoff(conv_lin(inpts + [reset * mem], "c", 0.0), cutoff)
    candidate = tf.tanh(conv_lin(inpts + [reset * mem], "c", 0.0))
  return gate * mem + (1 - gate) * candidate


CHOOSE_K = 256


def memory_call(q, l, nmaps, mem_size, vocab_size, num_gpus, update_mem):
  raise ValueError("Fill for experiments with additional memory structures.")


def memory_run(step, nmaps, mem_size, batch_size, vocab_size,
               global_step, do_training, update_mem, decay_factor, num_gpus,
               target_emb_weights, output_w, gpu_targets_tn, it):
  """Run memory."""
  q = step[:, 0, it, :]
  mlabels = gpu_targets_tn[:, it, 0]
  res, mask, mem_loss = memory_call(
      q, mlabels, nmaps, mem_size, vocab_size, num_gpus, update_mem)
  res = tf.gather(target_emb_weights, res) * tf.expand_dims(mask[:, 0], 1)

  # Mix gold and original in the first steps, 20% later.
  gold = tf.nn.dropout(tf.gather(target_emb_weights, mlabels), 0.7)
  use_gold = 1.0 - tf.cast(global_step, tf.float32) / (1000. * decay_factor)
  use_gold = tf.maximum(use_gold, 0.2) * do_training
  mem = tf.cond(tf.less(tf.random_uniform([]), use_gold),
                lambda: use_gold * gold + (1.0 - use_gold) * res,
                lambda: res)
  mem = tf.reshape(mem, [-1, 1, 1, nmaps])
  return mem, mem_loss, update_mem


@tf.RegisterGradient("CustomIdG")
def _custom_id_grad(_, grads):
  return grads


def quantize(t, quant_scale, max_value=1.0):
  """Quantize a tensor t with each element in [-max_value, max_value]."""
  t = tf.minimum(max_value, tf.maximum(t, -max_value))
  big = quant_scale * (t + max_value) + 0.5
  with tf.get_default_graph().gradient_override_map({"Floor": "CustomIdG"}):
    res = (tf.floor(big) / quant_scale) - max_value
  return res


def quantize_weights_op(quant_scale, max_value):
  ops = [v.assign(quantize(v, quant_scale, float(max_value)))
         for v in tf.trainable_variables()]
  return tf.group(*ops)


def autoenc_quantize(x, nbits, nmaps, do_training, layers=1):
  """Autoencoder into nbits vectors of bits, using noise and sigmoids."""
  enc_x = tf.reshape(x, [-1, nmaps])
  for i in xrange(layers - 1):
    enc_x = tf.layers.dense(enc_x, nmaps, name="autoenc_%d" % i)
  enc_x = tf.layers.dense(enc_x, nbits, name="autoenc_%d" % (layers - 1))
  noise = tf.truncated_normal(tf.shape(enc_x), stddev=2.0)
  dec_x = sigmoid_cutoff_12(enc_x + noise * do_training)
  dec_x = tf.reshape(dec_x, [-1, nbits])
  for i in xrange(layers):
    dec_x = tf.layers.dense(dec_x, nmaps, name="autodec_%d" % i)
  return tf.reshape(dec_x, tf.shape(x))


def make_dense(targets, noclass, low_param):
  """Move a batch of targets to a dense 1-hot representation."""
  low = low_param / float(noclass - 1)
  high = 1.0 - low * (noclass - 1)
  targets = tf.cast(targets, tf.int64)
  return tf.one_hot(targets, depth=noclass, on_value=high, off_value=low)


def reorder_beam(beam_size, batch_size, beam_val, output, is_first,
                 tensors_to_reorder):
  """Reorder to minimize beam costs."""
  # beam_val is [batch_size x beam_size]; let b = batch_size * beam_size
  # decided is len x b x a x b
  # output is b x out_size; step is b x len x a x b;
  outputs = tf.split(axis=0, num_or_size_splits=beam_size, value=tf.nn.log_softmax(output))
  all_beam_vals, all_beam_idx = [], []
  beam_range = 1 if is_first else beam_size
  for i in xrange(beam_range):
    top_out, top_out_idx = tf.nn.top_k(outputs[i], k=beam_size)
    cur_beam_val = beam_val[:, i]
    top_out = tf.Print(top_out, [top_out, top_out_idx, beam_val, i,
                                 cur_beam_val], "GREPO", summarize=8)
    all_beam_vals.append(top_out + tf.expand_dims(cur_beam_val, 1))
    all_beam_idx.append(top_out_idx)
  all_beam_idx = tf.reshape(tf.transpose(tf.concat(axis=1, values=all_beam_idx), [1, 0]),
                            [-1])
  top_beam, top_beam_idx = tf.nn.top_k(tf.concat(axis=1, values=all_beam_vals), k=beam_size)
  top_beam_idx = tf.Print(top_beam_idx, [top_beam, top_beam_idx],
                          "GREP", summarize=8)
  reordered = [[] for _ in xrange(len(tensors_to_reorder) + 1)]
  top_out_idx = []
  for i in xrange(beam_size):
    which_idx = top_beam_idx[:, i] * batch_size + tf.range(batch_size)
    top_out_idx.append(tf.gather(all_beam_idx, which_idx))
    which_beam = top_beam_idx[:, i] / beam_size  # [batch]
    which_beam = which_beam * batch_size + tf.range(batch_size)
    reordered[0].append(tf.gather(output, which_beam))
    for i, t in enumerate(tensors_to_reorder):
      reordered[i + 1].append(tf.gather(t, which_beam))
  new_tensors = [tf.concat(axis=0, values=t) for t in reordered]
  top_out_idx = tf.concat(axis=0, values=top_out_idx)
  return (top_beam, new_tensors[0], top_out_idx, new_tensors[1:])


class NeuralGPU(object):
  """Neural GPU Model."""

  def __init__(self, nmaps, vec_size, niclass, noclass, dropout,
               max_grad_norm, cutoff, nconvs, kw, kh, height, mem_size,
               learning_rate, min_length, num_gpus, num_replicas,
               grad_noise_scale, sampling_rate, act_noise=0.0, do_rnn=False,
               atrous=False, beam_size=1, backward=True, do_layer_norm=False,
               autoenc_decay=1.0):
    # Feeds for parameters and ops to update them.
    self.nmaps = nmaps
    if backward:
      self.global_step = tf.Variable(0, trainable=False, name="global_step")
      self.cur_length = tf.Variable(min_length, trainable=False)
      self.cur_length_incr_op = self.cur_length.assign_add(1)
      self.lr = tf.Variable(learning_rate, trainable=False)
      self.lr_decay_op = self.lr.assign(self.lr * 0.995)
    self.do_training = tf.placeholder(tf.float32, name="do_training")
    self.update_mem = tf.placeholder(tf.int32, name="update_mem")
    self.noise_param = tf.placeholder(tf.float32, name="noise_param")

    # Feeds for inputs, targets, outputs, losses, etc.
    self.input = tf.placeholder(tf.int32, name="inp")
    self.target = tf.placeholder(tf.int32, name="tgt")
    self.prev_step = tf.placeholder(tf.float32, name="prev_step")
    gpu_input = tf.split(axis=0, num_or_size_splits=num_gpus, value=self.input)
    gpu_target = tf.split(axis=0, num_or_size_splits=num_gpus, value=self.target)
    gpu_prev_step = tf.split(axis=0, num_or_size_splits=num_gpus, value=self.prev_step)
    batch_size = tf.shape(gpu_input[0])[0]

    if backward:
      adam_lr = 0.005 * self.lr
      adam = tf.train.AdamOptimizer(adam_lr, epsilon=1e-3)

      def adam_update(grads):
        return adam.apply_gradients(zip(grads, tf.trainable_variables()),
                                    global_step=self.global_step,
                                    name="adam_update")

    # When switching from Adam to SGD we perform reverse-decay.
    if backward:
      global_step_float = tf.cast(self.global_step, tf.float32)
      sampling_decay_exponent = global_step_float / 100000.0
      sampling_decay = tf.maximum(0.05, tf.pow(0.5, sampling_decay_exponent))
      self.sampling = sampling_rate * 0.05 / sampling_decay
    else:
      self.sampling = tf.constant(0.0)

    # Cache variables on cpu if needed.
    if num_replicas > 1 or num_gpus > 1:
      with tf.device("/cpu:0"):
        caching_const = tf.constant(0)
      tf.get_variable_scope().set_caching_device(caching_const.op.device)
      # partitioner = tf.variable_axis_size_partitioner(1024*256*4)
      # tf.get_variable_scope().set_partitioner(partitioner)

    def gpu_avg(l):
      if l[0] is None:
        for elem in l:
          assert elem is None
        return 0.0
      if len(l) < 2:
        return l[0]
      return sum(l) / float(num_gpus)

    self.length_tensor = tf.placeholder(tf.int32, name="length")

    with tf.device("/cpu:0"):
      emb_weights = tf.get_variable(
          "embedding", [niclass, vec_size],
          initializer=tf.random_uniform_initializer(-1.7, 1.7))
      if beam_size > 0:
        target_emb_weights = tf.get_variable(
            "target_embedding", [noclass, nmaps],
            initializer=tf.random_uniform_initializer(-1.7, 1.7))
      e0 = tf.scatter_update(emb_weights,
                             tf.constant(0, dtype=tf.int32, shape=[1]),
                             tf.zeros([1, vec_size]))
      output_w = tf.get_variable("output_w", [nmaps, noclass], tf.float32)

    def conv_rate(layer):
      if atrous:
        return 2**layer
      return 1

    # pylint: disable=cell-var-from-loop
    def enc_step(step):
      """Encoder step."""
      if autoenc_decay < 1.0:
        quant_step = autoenc_quantize(step, 16, nmaps, self.do_training)
        if backward:
          exp_glob = tf.train.exponential_decay(1.0, self.global_step - 10000,
                                                1000, autoenc_decay)
          dec_factor = 1.0 - exp_glob  # * self.do_training
          dec_factor = tf.cond(tf.less(self.global_step, 10500),
                               lambda: tf.constant(0.05), lambda: dec_factor)
        else:
          dec_factor = 1.0
        cur = tf.cond(tf.less(tf.random_uniform([]), dec_factor),
                      lambda: quant_step, lambda: step)
      else:
        cur = step
      if dropout > 0.0001:
        cur = tf.nn.dropout(cur, keep_prob)
      if act_noise > 0.00001:
        cur += tf.truncated_normal(tf.shape(cur)) * act_noise_scale
      # Do nconvs-many CGRU steps.
      if do_jit and tf.get_variable_scope().reuse:
        with jit_scope():
          for layer in xrange(nconvs):
            cur = conv_gru([], cur, kw, kh, nmaps, conv_rate(layer),
                           cutoff, "ecgru_%d" % layer, do_layer_norm)
      else:
        for layer in xrange(nconvs):
          cur = conv_gru([], cur, kw, kh, nmaps, conv_rate(layer),
                         cutoff, "ecgru_%d" % layer, do_layer_norm)
      return cur

    zero_tgt = tf.zeros([batch_size, nmaps, 1])
    zero_tgt.set_shape([None, nmaps, 1])

    def dec_substep(step, decided):
      """Decoder sub-step."""
      cur = step
      if dropout > 0.0001:
        cur = tf.nn.dropout(cur, keep_prob)
      if act_noise > 0.00001:
        cur += tf.truncated_normal(tf.shape(cur)) * act_noise_scale
      # Do nconvs-many CGRU steps.
      if do_jit and tf.get_variable_scope().reuse:
        with jit_scope():
          for layer in xrange(nconvs):
            cur = conv_gru([decided], cur, kw, kh, nmaps, conv_rate(layer),
                           cutoff, "dcgru_%d" % layer, do_layer_norm)
      else:
        for layer in xrange(nconvs):
          cur = conv_gru([decided], cur, kw, kh, nmaps, conv_rate(layer),
                         cutoff, "dcgru_%d" % layer, do_layer_norm)
      return cur
    # pylint: enable=cell-var-from-loop

    def dec_step(step, it, it_int, decided, output_ta, tgts,
                 mloss, nupd_in, out_idx, beam_cost):
      """Decoder step."""
      nupd, mem_loss = 0, 0.0
      if mem_size > 0:
        it_incr = tf.minimum(it+1, length - 1)
        mem, mem_loss, nupd = memory_run(
            step, nmaps, mem_size, batch_size, noclass, self.global_step,
            self.do_training, self.update_mem, 10, num_gpus,
            target_emb_weights, output_w, gpu_targets_tn, it_incr)
      step = dec_substep(step, decided)
      output_l = tf.expand_dims(tf.expand_dims(step[:, it, 0, :], 1), 1)
      # Calculate argmax output.
      output = tf.reshape(output_l, [-1, nmaps])
      # pylint: disable=cell-var-from-loop
      output = tf.matmul(output, output_w)
      if beam_size > 1:
        beam_cost, output, out, reordered = reorder_beam(
            beam_size, batch_size, beam_cost, output, it_int == 0,
            [output_l, out_idx, step, decided])
        [output_l, out_idx, step, decided] = reordered
      else:
        # Scheduled sampling.
        out = tf.multinomial(tf.stop_gradient(output), 1)
        out = tf.to_int32(tf.squeeze(out, [1]))
      out_write = output_ta.write(it, output_l[:batch_size, :, :, :])
      output = tf.gather(target_emb_weights, out)
      output = tf.reshape(output, [-1, 1, nmaps])
      output = tf.concat(axis=1, values=[output] * height)
      tgt = tgts[it, :, :, :]
      selected = tf.cond(tf.less(tf.random_uniform([]), self.sampling),
                         lambda: output, lambda: tgt)
      # pylint: enable=cell-var-from-loop
      dec_write = place_at14(decided, tf.expand_dims(selected, 1), it)
      out_idx = place_at13(
          out_idx, tf.reshape(out, [beam_size * batch_size, 1, 1]), it)
      if mem_size > 0:
        mem = tf.concat(axis=2, values=[mem] * height)
        dec_write = place_at14(dec_write, mem, it_incr)
      return (step, dec_write, out_write, mloss + mem_loss, nupd_in + nupd,
              out_idx, beam_cost)

    # Main model construction.
    gpu_outputs = []
    gpu_losses = []
    gpu_grad_norms = []
    grads_list = []
    gpu_out_idx = []
    self.after_enc_step = []
    for gpu in xrange(num_gpus):  # Multi-GPU towers, average gradients later.
      length = self.length_tensor
      length_float = tf.cast(length, tf.float32)
      if gpu > 0:
        tf.get_variable_scope().reuse_variables()
      gpu_outputs.append([])
      gpu_losses.append([])
      gpu_grad_norms.append([])
      with tf.name_scope("gpu%d" % gpu), tf.device("/gpu:%d" % gpu):
        # Main graph creation loop.
        data.print_out("Creating model.")
        start_time = time.time()

        # Embed inputs and calculate mask.
        with tf.device("/cpu:0"):
          tgt_shape = tf.shape(tf.squeeze(gpu_target[gpu], [1]))
          weights = tf.where(tf.squeeze(gpu_target[gpu], [1]) > 0,
                             tf.ones(tgt_shape), tf.zeros(tgt_shape))

          # Embed inputs and targets.
          with tf.control_dependencies([e0]):
            start = tf.gather(emb_weights, gpu_input[gpu])  # b x h x l x nmaps
            gpu_targets_tn = gpu_target[gpu]  # b x 1 x len
            if beam_size > 0:
              embedded_targets_tn = tf.gather(target_emb_weights,
                                              gpu_targets_tn)
              embedded_targets_tn = tf.transpose(
                  embedded_targets_tn, [2, 0, 1, 3])  # len x b x 1 x nmaps
              embedded_targets_tn = tf.concat(axis=2, values=[embedded_targets_tn] * height)

        # First image comes from start by applying convolution and adding 0s.
        start = tf.transpose(start, [0, 2, 1, 3])  # Now b x len x h x vec_s
        first = conv_linear(start, 1, 1, vec_size, nmaps, 1, True, 0.0, "input")
        first = layer_norm(first, nmaps, "input")

        # Computation steps.
        keep_prob = dropout * 3.0 / tf.sqrt(length_float)
        keep_prob = 1.0 - self.do_training * keep_prob
        act_noise_scale = act_noise * self.do_training

        # Start with a convolutional gate merging previous step.
        step = conv_gru([gpu_prev_step[gpu]], first,
                        kw, kh, nmaps, 1, cutoff, "first", do_layer_norm)

        # This is just for running a baseline RNN seq2seq model.
        if do_rnn:
          self.after_enc_step.append(step)  # Not meaningful here, but needed.
          def lstm_cell():
            return tf.contrib.rnn.BasicLSTMCell(height * nmaps)
          cell = tf.contrib.rnn.MultiRNNCell(
              [lstm_cell() for _ in range(nconvs)])
          with tf.variable_scope("encoder"):
            encoder_outputs, encoder_state = tf.nn.dynamic_rnn(
                cell, tf.reshape(step, [batch_size, length, height * nmaps]),
                dtype=tf.float32, time_major=False)

          # Attention.
          attn = tf.layers.dense(
              encoder_outputs, height * nmaps, name="attn1")

          # pylint: disable=cell-var-from-loop
          @function.Defun(noinline=True)
          def attention_query(query, attn_v):
            vecs = tf.tanh(attn + tf.expand_dims(query, 1))
            mask = tf.reduce_sum(vecs * tf.reshape(attn_v, [1, 1, -1]), 2)
            mask = tf.nn.softmax(mask)
            return tf.reduce_sum(encoder_outputs * tf.expand_dims(mask, 2), 1)

          with tf.variable_scope("decoder"):
            def decoder_loop_fn(state__prev_cell_out__unused, cell_inp__cur_tgt):
              """Decoder loop function."""
              state, prev_cell_out, _ = state__prev_cell_out__unused
              cell_inp, cur_tgt = cell_inp__cur_tgt
              attn_q = tf.layers.dense(prev_cell_out, height * nmaps,
                                       name="attn_query")
              attn_res = attention_query(attn_q, tf.get_variable(
                  "attn_v", [height * nmaps],
                  initializer=tf.random_uniform_initializer(-0.1, 0.1)))
              concatenated = tf.reshape(tf.concat(axis=1, values=[cell_inp, attn_res]),
                                        [batch_size, 2 * height * nmaps])
              cell_inp = tf.layers.dense(
                  concatenated, height * nmaps, name="attn_merge")
              output, new_state = cell(cell_inp, state)

              mem_loss = 0.0
              if mem_size > 0:
                res, mask, mem_loss = memory_call(
                    output, cur_tgt, height * nmaps, mem_size, noclass,
                    num_gpus, self.update_mem)
                res = tf.gather(target_emb_weights, res)
                res *= tf.expand_dims(mask[:, 0], 1)
                output = tf.layers.dense(
                    tf.concat(axis=1, values=[output, res]), height * nmaps, name="rnnmem")

              return new_state, output, mem_loss
            # pylint: enable=cell-var-from-loop
            gpu_targets = tf.squeeze(gpu_target[gpu], [1])  # b x len
            gpu_tgt_trans = tf.transpose(gpu_targets, [1, 0])
            dec_zero = tf.zeros([batch_size, 1], dtype=tf.int32)
            dec_inp = tf.concat(axis=1, values=[dec_zero, gpu_targets])
            dec_inp = dec_inp[:, :length]
            embedded_dec_inp = tf.gather(target_emb_weights, dec_inp)
            embedded_dec_inp_proj = tf.layers.dense(
                embedded_dec_inp, height * nmaps, name="dec_proj")
            embedded_dec_inp_proj = tf.transpose(embedded_dec_inp_proj,
                                                 [1, 0, 2])
            init_vals = (encoder_state,
                         tf.zeros([batch_size, height * nmaps]), 0.0)
            _, dec_outputs, mem_losses = tf.scan(
                decoder_loop_fn, (embedded_dec_inp_proj, gpu_tgt_trans),
                initializer=init_vals)
          mem_loss = tf.reduce_mean(mem_losses)
          outputs = tf.layers.dense(dec_outputs, nmaps, name="out_proj")
          # Final convolution to get logits, list outputs.
          outputs = tf.matmul(tf.reshape(outputs, [-1, nmaps]), output_w)
          outputs = tf.reshape(outputs, [length, batch_size, noclass])
          gpu_out_idx.append(tf.argmax(outputs, 2))
        else:  # Here we go with the Neural GPU.
          # Encoder.
          enc_length = length
          step = enc_step(step)  # First step hard-coded.
          # pylint: disable=cell-var-from-loop
          i = tf.constant(1)
          c = lambda i, _s: tf.less(i, enc_length)
          def enc_step_lambda(i, step):
            with tf.variable_scope(tf.get_variable_scope(), reuse=True):
              new_step = enc_step(step)
            return (i + 1, new_step)
          _, step = tf.while_loop(
              c, enc_step_lambda, [i, step],
              parallel_iterations=1, swap_memory=True)
          # pylint: enable=cell-var-from-loop

          self.after_enc_step.append(step)

          # Decoder.
          if beam_size > 0:
            output_ta = tf.TensorArray(
                dtype=tf.float32, size=length, dynamic_size=False,
                infer_shape=False, name="outputs")
            out_idx = tf.zeros([beam_size * batch_size, length, 1],
                               dtype=tf.int32)
            decided_t = tf.zeros([beam_size * batch_size, length,
                                  height, vec_size])

            # Prepare for beam search.
            tgts = tf.concat(axis=1, values=[embedded_targets_tn] * beam_size)
            beam_cost = tf.zeros([batch_size, beam_size])
            step = tf.concat(axis=0, values=[step] * beam_size)
            # First step hard-coded.
            step, decided_t, output_ta, mem_loss, nupd, oi, bc = dec_step(
                step, 0, 0, decided_t, output_ta, tgts, 0.0, 0, out_idx,
                beam_cost)
            tf.get_variable_scope().reuse_variables()
            # pylint: disable=cell-var-from-loop
            def step_lambda(i, step, dec_t, out_ta, ml, nu, oi, bc):
              with tf.variable_scope(tf.get_variable_scope(), reuse=True):
                s, d, t, nml, nu, oi, bc = dec_step(
                    step, i, 1, dec_t, out_ta, tgts, ml, nu, oi, bc)
              return (i + 1, s, d, t, nml, nu, oi, bc)
            i = tf.constant(1)
            c = lambda i, _s, _d, _o, _ml, _nu, _oi, _bc: tf.less(i, length)
            _, step, _, output_ta, mem_loss, nupd, out_idx, _ = tf.while_loop(
                c, step_lambda,
                [i, step, decided_t, output_ta, mem_loss, nupd, oi, bc],
                parallel_iterations=1, swap_memory=True)
            # pylint: enable=cell-var-from-loop
            gpu_out_idx.append(tf.squeeze(out_idx, [2]))
            outputs = output_ta.stack()
            outputs = tf.squeeze(outputs, [2, 3])  # Now l x b x nmaps
          else:
            # If beam_size is 0 or less, we don't have a decoder.
            mem_loss = 0.0
            outputs = tf.transpose(step[:, :, 1, :], [1, 0, 2])
            gpu_out_idx.append(tf.argmax(outputs, 2))

          # Final convolution to get logits, list outputs.
          outputs = tf.matmul(tf.reshape(outputs, [-1, nmaps]), output_w)
          outputs = tf.reshape(outputs, [length, batch_size, noclass])
        gpu_outputs[gpu] = tf.nn.softmax(outputs)

        # Calculate cross-entropy loss and normalize it.
        targets_soft = make_dense(tf.squeeze(gpu_target[gpu], [1]),
                                  noclass, 0.1)
        targets_soft = tf.reshape(targets_soft, [-1, noclass])
        targets_hard = make_dense(tf.squeeze(gpu_target[gpu], [1]),
                                  noclass, 0.0)
        targets_hard = tf.reshape(targets_hard, [-1, noclass])
        output = tf.transpose(outputs, [1, 0, 2])
        xent_soft = tf.reshape(tf.nn.softmax_cross_entropy_with_logits(
            logits=tf.reshape(output, [-1, noclass]), labels=targets_soft),
                               [batch_size, length])
        xent_hard = tf.reshape(tf.nn.softmax_cross_entropy_with_logits(
            logits=tf.reshape(output, [-1, noclass]), labels=targets_hard),
                               [batch_size, length])
        low, high = 0.1 / float(noclass - 1), 0.9
        const = high * tf.log(high) + float(noclass - 1) * low * tf.log(low)
        weight_sum = tf.reduce_sum(weights) + 1e-20
        true_perp = tf.reduce_sum(xent_hard * weights) / weight_sum
        soft_loss = tf.reduce_sum(xent_soft * weights) / weight_sum
        perp_loss = soft_loss + const
        # Final loss: cross-entropy + shared parameter relaxation part + extra.
        mem_loss = 0.5 * tf.reduce_mean(mem_loss) / length_float
        total_loss = perp_loss + mem_loss
        gpu_losses[gpu].append(true_perp)

        # Gradients.
        if backward:
          data.print_out("Creating backward pass for the model.")
          grads = tf.gradients(
              total_loss, tf.trainable_variables(),
              colocate_gradients_with_ops=True)
          for g_i, g in enumerate(grads):
            if isinstance(g, tf.IndexedSlices):
              grads[g_i] = tf.convert_to_tensor(g)
          grads, norm = tf.clip_by_global_norm(grads, max_grad_norm)
          gpu_grad_norms[gpu].append(norm)
          for g in grads:
            if grad_noise_scale > 0.001:
              g += tf.truncated_normal(tf.shape(g)) * self.noise_param
          grads_list.append(grads)
        else:
          gpu_grad_norms[gpu].append(0.0)
        data.print_out("Created model for gpu %d in %.2f s."
                       % (gpu, time.time() - start_time))

    self.updates = []
    self.after_enc_step = tf.concat(axis=0, values=self.after_enc_step)  # Concat GPUs.
    if backward:
      tf.get_variable_scope()._reuse = False
      tf.get_variable_scope().set_caching_device(None)
      grads = [gpu_avg([grads_list[g][i] for g in xrange(num_gpus)])
               for i in xrange(len(grads_list[0]))]
      update = adam_update(grads)
      self.updates.append(update)
    else:
      self.updates.append(tf.no_op())

    self.losses = [gpu_avg([gpu_losses[g][i] for g in xrange(num_gpus)])
                   for i in xrange(len(gpu_losses[0]))]
    self.out_idx = tf.concat(axis=0, values=gpu_out_idx)
    self.grad_norms = [gpu_avg([gpu_grad_norms[g][i] for g in xrange(num_gpus)])
                       for i in xrange(len(gpu_grad_norms[0]))]
    self.outputs = [tf.concat(axis=1, values=[gpu_outputs[g] for g in xrange(num_gpus)])]
    self.quantize_op = quantize_weights_op(512, 8)
    if backward:
      self.saver = tf.train.Saver(tf.global_variables(), max_to_keep=10)

  def step(self, sess, inp, target, do_backward_in, noise_param=None,
           beam_size=2, eos_id=2, eos_cost=0.0, update_mem=None, state=None):
    """Run a step of the network."""
    batch_size, height, length = inp.shape[0], inp.shape[1], inp.shape[2]
    do_backward = do_backward_in
    train_mode = True
    if do_backward_in is None:
      do_backward = False
      train_mode = False
    if update_mem is None:
      update_mem = do_backward
    feed_in = {}
    # print "    feeding sequences of length %d" % length
    if state is None:
      state = np.zeros([batch_size, length, height, self.nmaps])
    feed_in[self.prev_step.name] = state
    feed_in[self.length_tensor.name] = length
    feed_in[self.noise_param.name] = noise_param if noise_param else 0.0
    feed_in[self.do_training.name] = 1.0 if do_backward else 0.0
    feed_in[self.update_mem.name] = 1 if update_mem else 0
    if do_backward_in is False:
      feed_in[self.sampling.name] = 0.0
    index = 0  # We're dynamic now.
    feed_out = []
    if do_backward:
      feed_out.append(self.updates[index])
      feed_out.append(self.grad_norms[index])
    if train_mode:
      feed_out.append(self.losses[index])
    feed_in[self.input.name] = inp
    feed_in[self.target.name] = target
    feed_out.append(self.outputs[index])
    if train_mode:
      # Make a full-sequence training step with one call to session.run.
      res = sess.run([self.after_enc_step] + feed_out, feed_in)
      after_enc_state, res = res[0], res[1:]
    else:
      # Make a full-sequence decoding step with one call to session.run.
      feed_in[self.sampling.name] = 1.1  # Sample every time.
      res = sess.run([self.after_enc_step, self.out_idx] + feed_out, feed_in)
      after_enc_state, out_idx = res[0], res[1]
      res = [res[2][l] for l in xrange(length)]
      outputs = [out_idx[:, i] for i in xrange(length)]
      cost = [0.0 for _ in xrange(beam_size * batch_size)]
      seen_eos = [0 for _ in xrange(beam_size * batch_size)]
      for idx, logit in enumerate(res):
        best = outputs[idx]
        for b in xrange(batch_size):
          if seen_eos[b] > 1:
            cost[b] -= eos_cost
          else:
            cost[b] += np.log(logit[b][best[b]])
          if best[b] in [eos_id]:
            seen_eos[b] += 1
      res = [[-c for c in cost]] + outputs
    # Collect and output results.
    offset = 0
    norm = None
    if do_backward:
      offset = 2
      norm = res[1]
    if train_mode:
      outputs = res[offset + 1]
      outputs = [outputs[l] for l in xrange(length)]
    return res[offset], outputs, norm, after_enc_state